<p>Shooting method</p>

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Shooting Method

Solve this Boundary Values Problem using the Shooting method

ode x y x 2 diff 12 / x y x diff * + x y + 5 - :

x.0 x.1 12 mat 1 - 612 mat :

y.0 y.1 12 mat 7312 mat :

Get the symbolic solution for check

x y.s ode x.0 y y.0 ≡ x.1 y y.1 ≡ 31 sys dsolve x y subs evalf maple :

The goal is get the slope at x.0 for use with a numerical ode solvers as the initial condition

x.0 y.s x.0 diff 27.5704 -

Convert to a system

x y D y 2 el y 2 el 2 / - y 1 el - 5 + 21 mat :

Use an ode solver

y'.0 sol y.0 y'.0 21 mat x.0 x.1 N 1 - D al_rkckadapt :

N 100 :

Equation to solve

y'.0 Eq y'.0 sol N 2 el y.1 - :

Guess for a solution

y'.0 10 - :

Solve, this is: shoot and see if holds

y'.0 y'.0 Eq al_nleqsolve 1 el : 27.5704 -

Plot and check

XY y'.0 sol : X Y 12 mat XY 1 col XY 2 col 12 mat : 21 sys

X Y . augment x y.s y'.0 x x.0 - ( * y.0 + 3 1 sys

Y X y.s vectorize - normi 7.39 108 -^*

x.0 y.s x.0 diff y'.0 - abs 1.1534 107 -^*

Alvaro